I don't believe you can do a Boot Camp windows install on an external hard drive; Boot Camp won't partition or otherwise function with an external drive. Have not tried it personally, but have seen this question come up several times.
If you need to run Windows in Boot Camp, which it sounds like you do because of your gaming interest, you'll need to do the install on the iMac's internal HD.
On your other questions:
With only 4 GB of RAM, 32-bit should be fine. If you add more RAM, then a 64-bit install might make more sense as the 32-bit version can only access 3 GB.
8 GB of RAM ALWAYS helps.
At least on the margin. If you can install extra RAM, then 64-bit Windows would access more. More RAM is always "mo' betta." Just a question of where to spend your $$.
Yes, you'll need AV software for the Windows side - but nothing that infects your Windows partition will affect the Mac side.
And yes, it's pretty easy but definitely back everything up first. Find and print out the Apple Boot Camp installation guide and follow it step by step - some of the aspects are counter-intuitive.
Can't comment on the specific games but generally with a boot camp installation, the windows games run as well on the Mac as they would on a similarly-configured Windows PC. You didn't specify what video adapter you had - that's likely to be the limiting factor rather to gaming performance (along with system RAM) more than anything else.
These are all the "short answers." The "long and better" answers are found in the 2 stickies at the top of this forum. HIGHLY RECOMMEND reading them before attempting the Boot Camp install.
Cheers